In Zero Intermediate Frequency (ZIF) and Direct Conversion Receivers, it is desirable to phase-lock (or frequency lock) the Local Oscillator (LO) to the incoming signal. This is because phase-locking will allow the receiver to track the central frequency of the incoming signal and eliminates this reference oscillator error (it constraints the offsets and beat notes caused by frequency offset of LO and incoming signal to a subaudible frequency). The phase-locking used with ZIF receivers needs to include a frequency offset which is used to avoid false carrier or self-quieting problem. Indeed, this slight frequency offset is used by a high pass filter centered very close to DC to allow the desired signal to pass through without the DC components that would otherwise be treated as false carriers. To accomplish this objective of locking with a frequency offset, traditional ZIF receivers use up-conversion mixers to increase the frequency from a baseband to an IF and therefore facilitating the phase locking. As can be appreciated, this up-conversion requires mixers and filters which would add to the cost of the receiver. To overcome this problem, a direct conversion receiver is needed that can phase-lock with an incoming signal with a frequency offset without any up-conversion.